As mike says you can do the battery mod (http://www.marshalljmpmodshop.net/miscellaneous_parts_and_replacement_tubes.htm) scroll down a bit you'll find it.
When I went looking for a battery holder for my MP2 (MP1 mounts flat to the PCB, MP2 is vertical), I found there are lots of batteries with the wires already attached ready to solder in (common for PC mother boards etc) and this is the cheapest option. As Mike says, they seem to last about 25 + years so soldering in one of these makes sense (to me anyway LoL).
So your issue is definitely battery is flat (like the guys have said). The battery powers the ram chip where the patches are stored. The factory presets are programmed in the EPROM (what version is your MP1, it will say at start up in the display) then you load them into ram with the factory restore. When you power down, the battery takes over keeping the ram powered.
IIRC MJMP said the battery needs to still have <2.7 volts of charge left to work.
So the battery you want is a CR2032 3v with legs attached. You can get them from electronics stores (or probably computer store (where they build PCs etc)). How are you with a soldering Iron BTW ??